A "wag" is a guess at an answer, the result of a numerical hunch. Because of its similarity to the verb "wag" (an indistinct shaking) it stands as a shorthand for a hand-waving answer. The phrase is often rendered in verb form as "take a wag", e.g.We've got three different numbers, each equally invalid; we'll have to take a wag at it.

WAGs can be good or bad, depending on context. If you know the true measurement is between 10m and 20m and so you throw 15m into the equation, then you've made a WAG. If your equation doesn't require any more precision than that, then it's a good WAG. However, if you need to know the mass to within a millimeter, then don't take a WAG.

A man full of sport and humor; a ludicrous fellow; a humorist; a wit; a joker.

We wink at wags when they offend.
Dryden.

A counselor never pleaded without a piece of pack thread in his hand, which he used to twist about a finger all the while he was speaking; the wags used to call it the thread of his discourse.
Addison.